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CoursesNichtlineare Dynamik und Kontrolle

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Important Information

The lectures will take place online via Zoom.

Please register in ISIS ("Nichtlineare Dynamik und Kontrolle") to access the digital material and zoom link.

The first lecture will take place on April 12 at 12:15. There will be no lecture on May 25 (SIAM Conference).

Nonlinear Dynamics and Control

Wahlpflichtveranstaltung 3233 L 120 im Sommersemester 2021:

Lectures (SAP number 3233 L 120):

Lecturer: Prof. Dr. Anna Mandel-Zakharova,

Mo 12:15 - 13:45 via Zoom

Tue 12:15 - 13:45 via Zoom

Tutorials (SAP number 3233 L 121):

Tutor: Dr. Ling-Na Wu,

Tue 14:15 - 15:45 via Zoom

The course is suitable for physics students (BSc, MSc), for Master students of natural science and Engineering and for interested members of the SFB 910.
The course is especially suitable for Master students interested in theoretical research and those who want to do a master thesis in the fields of nonlinear dynamics and complex networks. The course addresses current research topics in these fields.

The course will be given in English.

The following course in Summer Term 2021 is recommended:
Nichtlineare Dynamik in komplexen Netzwerken (Seminar), 3233 L 611: Noise-induced phenomena in complex networks

Module assignment (Modulzuordnung)

This course (lecture and tutorial) can be completed as
* a theoretical elective module (theoretisches Wahlpflichtmodul, StuPO 2018/19), or as
* a specialization in the basic-oriented module Theoretical Physics V/VI - Nonlinear Dynamics and Control (grundlagenorientiertes Modul Theoretische Physik V/VI - Nichtlineare Dynamik und Kontrolle) or
* in the application-oriented module Theoretical Physics VI (anwendungsorientiertes Modul Theoretische Physik VI).

Also, this course (lecture and tutorial) can be completed as a physics elective course (physikalisches Wahlpflichtfach) together with a seminar or special lecture from theoretical physics (in consultation with the lecturer) as a elective module Nonlinear Dynamics and Control (als Wahlpflichtfach Nichtlineare Dynamik und Kontrolle, StuPO 2008).

Scheinkriterien

  • 50% der Punkte aus den Übungszetteln (Abgabe in Dreiergruppen),
    aktive Teilnahme am Tutorium
  • Bearbeitung und Vorstellung eines Projektes (Projektvorstellung in der letzten Vorlesungswoche)

Die Scheine werden elektronisch an das Prüfungsamt übermittelt.

Lectures

The lectures cover the main concepts of nonlinear dynamics and control. First, the basic ideas of nonlinear dynamics, such as the description of nonlinear systems, stability analysis, bifurcations, and attractors will be introduced. Further, we will discuss the main concepts of the synchronization theory and apply the tools of nonlinear dynamics to analyze synchronization phenomena. Special attention will be paid to partial synchronization patterns. Synchronization is one of the fundamental phenomena in nature. Fireflies flashing in unison, the coordinated firing of pacemaker cells in our hearts, fish swimming in a synchronized swarm – these are just a few real-world examples of self-organization. We will discuss synchronization in various systems ranging from periodic oscillators to stochastic systems, from two coupled units to complex networks. Various applications in different fields of science including physics, chemistry, biology, and engineering will be discussed.

Literature

Books:

  • A. Zakharova, Chimera Patterns in Networks: Interplay between Dynamics, Structure, Noise, and Delay, Series: Understanding Complex Systems, Springer (2020)
  • S. Boccaletti, A. N. Pisarchik, C. I. del Genio and A. Amann, Synchronization: From Coupled Systems to Complex Networks, Cambridge University Press (2018)
  • V. S. Anishchenko, T. Vadivasova and G. Strelkova, Deterministic Nonlinear Systems, Springer Series in Synergetics, Springer (2014)
  • S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, Complex networks: Structure and dynamics, Phys. Rep. 424, 4-5, 175 (2006)
  • S. Strogatz, Sync: The Emerging Science of Spontaneous Order, Hyperion Press, New York (2003)
  • A. Pikovsky, M.G. Rosenblum and J. Kurths, Synchronization: a universal concept in nonlinear sciences, Cambridge University Press (2001)
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